Formally show the relationship between a bond yield and bond price for a zero coupon bond (using the notation from lectures). Find the derivative of the yield with respect to the price and comment on the relationship. a) [10] b) Assume that investors require a risk premium on top of the return given by the pure Expectations Theory to hold long-term assets. Today's one-year bond rate is 2%, the expected one-year rate in year 2 is 3%, in year 3 it is 4%, in year 4 it is 5% and in year 5 it is 6%. If today's 5-year bond rate is 3.5%, estimate the risk premium that investors require to hold a 5-year bond c) Set out two reasons why a risk premium might be required in this case. 17)